Lecture 17: Noise in gene expression
Today:
The models we’ve discussed so far are “deterministic”
Bacterial growth:
“deterministic”: the end result is completely determined by the initial conditions.
The models we’ve discussed so far are “deterministic”
“deterministic”: the end result is completely determined by the initial conditions.
Gene expression:
But real biological systems do things like this…
Dunlop, et al. (2008) doi:10.1038/ng.281
Gene 1
Gene 1
And this…
Süel, et al. (2006), doi:10.1038/nature04588
Many components of gene expression are present at very low copy numbers
Gene/DNA: ~1-2 copies per cell
RNA polymerase: ~1000s
Transcription factors: ~10s-1000s
mRNA: ~0.1-10
ribosomes: ~1000s
Highly susceptible to random fluctuations.
transcription
translation
Remember the chocolate chip cookies
90 chocolate chips, 20 cookies → 4.5 chips/cookie
300 chocolate chips, 21 cookies → 14.3 chips/cookie
Chocolate chip cookies
Within each population, the cookies went through an identical process.
But due to pure randomness or “stochasticity”, we have variation in the number of chips per cookie.
This “noise” in # of chocolate chips is unavoidable unless we create an extra process to control it (e.g. precisely counting chips and making each cookie one-by-one).
mean chip #
substantial variation relative to mean!
Deterministic vs. stochastic
Deterministic: outcome determined by initial conditions, dynamics, and/or agent actions
Example: chess
Example: Dungeons & Dragons
Stochastic: inevitable randomness
Deterministic vs. stochastic
Deterministic: outcome determined by initial conditions, dynamics, and/or agent actions
Example: roller coaster
Example: bumper cars
Stochastic: inevitable randomness
“Noise”
protein concentration
time
noisy signal
non-noisy signal
Cells may want to suppress noise
Developing fly embryo
Failure to suppress noise would result in different developmental outcomes every time!
Noise could also be useful
mRNAs in single cells (5 per cell on average)
For example, cells with a large number of mRNAs could enter a different phenotypic state
Noise could also be useful
mRNAs in single cells (5 per cell on average)
For example, cells with a large number of mRNAs could enter a different phenotypic state
↑ Heterogeneous cell states! ↑
PhET video
How might noise manifest itself in bacterial gene expression?
mRNA:
The life of an mRNA:
Comes into existence
RNases and ribosomes compete for the mRNA
RNase
ribosome
⚔️
Ribosomes quickly translate as many proteins as they can before RNases takes out the mRNA—”burstiness”
Time
Protein #
Modeling “bursty”/noisy gene expression
Create a model that explicitly takes into account the low numbers/noise in each of these processes!
(Gillespie algorithm)
Stochastic model of the Lac system in E. coli:
Cells with exactly the same conditions can have different gene expression dynamics!
Time
A large variety of trajectories for cells starting from the same state!
Time
How can we measure this noise experimentally??
There are two components to gene expression noise
Ribosome
RNA polymerase
.
.
.
Fluctuations in the concentrations of these components will lead to fluctuations in gene expression, but should affect all genes in the same way.
Imagine we have a population of cells where somehow the extrinsic noise is 0. They all have exactly the same concentration of ribosomes, regulatory proteins, etc.
There will still be variation in the concentration of the protein. This is due to the noise intrinsic to the expression of this gene!
How do we separate intrinsic noise from extrinsic noise and study the effects of each?
An experimental system to measure intrinsic and extrinsic noise in E. coli
YFP
CFP
Exact same promoters
Different fluorescent proteins
The two gene copies are equidistant from the origin of replication to avoid copy number variation during genome replication!
Varying activity of the same gene
High green copy number/low red copy number
High red copy number/low green copy number
High both
Low both
High extrinsic noise, low intrinsic noise
Signal from two copies within one cell
copy 1
copy 2
Population of cells dominated by extrinsic noise
High intrinsic noise
copy 1
copy 2
Population of cells dominated by intrinsic noise
Quantifying noise
YFP
CFP
Squared difference between c and y
Average difference
Normalize by average levels for noise
Quantifying noise
Average product
Subtract off product of averages
Normalize by average levels for noise
Quantifying noise
Two different strains
Intuitively, we expect genes that are transcribed at a low level to be noisier. Is that the case?
Strains with a range of transcription rates
Transcription rate
Noise?
YFP
CFP
lacI
YFP
CFP
lacI
lacI
YFP
CFP
lacI
IPTG
Noise vs. transcription level
How do we expect intrinsic noise to depend quantitatively on transcription rate?
For low transcription rate, how are mRNAs distributed?
Intrinsic and extrinsic noise vs. transcription
YFP
CFP
lacI
IPTG
Increasing IPTG concentration
Poisson fit
Intrinsic and extrinsic noise vs. transcription
YFP
CFP
lacI
IPTG
Increasing IPTG concentration
Poisson fit
When transcription is low, identical cells can be variable due to intrinsic low-copy-number noise!
When transcription is higher, identical cells can be variable due to extrinsic noise!
Where is there a maximum in the measured extrinsic noise?
Increasing IPTG concentration
IPTG works be inactivating LacI.
At low IPTG concentration, increasing noise with increasing IPTG may be due to variations in LacI concentration.
Once IPTG is extremely high, all LacIs are inactivated regardless of their concentration, leading to low noise.
What have we learned?